Issues in quantifying variability from a dynamical systems perspective

Variability is a critical aspect of a dynamical systems analysis. Because t here are a number of numerical techniques that can be used in such an analy sis, the calculation of variability has several issues that must be address ed. The purpose of this paper is to present a variety of quantitative metho ds for investigating variability from a dynamical systems perspective. The paper is divided into two major sections covering discrete and continuous m ethods. Each of these sections is subdivided into two sections. Within disc rete methods, we discuss, first, the calculation of the discrete relative p hase from a time-series history of two parameters and, second, the use of r eturn maps. Using continuous methods, we present procedures for using angle -angle plots in the evaluation of relative phase. We then discuss the use o f phase plots in the calculation of the continuous relative phase. Each of these methods presents unique problems for the re searcher and the method t o be used is determined by the nature of the question asked.